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Modelling hydraulic jump using the bubbly two-phase flow method

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Abstract

Hydraulic jumps have complex flow structures, characterised by strong turbulence and large air contents. It is difficult to numerically predict the flows. It is necessary to bolster the existing computer models to emphasise the gas phase in hydraulic jumps, and avoid the pitfall of treating the phenomenon as a single-phase water flow. This paper aims to improve predictions of hydraulic jumps as bubbly two-phase flow. We allow for airflow above the free surface and air mass entrained across it. We use the Reynolds-averaged Navier–Stokes equations to describe fluid motion, the volume of fluid method to track the interface, and the k–ε model for turbulence closure. A shear layer is shown to form between the bottom jet flow and the upper recirculation flow. The key to success in predicting the jet flow lies in formulating appropriate bottom boundary conditions. The majority of entrained air bubbles are advected downstream through the shear layer. Predictions of the recirculation region’s length and air volume fraction within the layer are validated by available measurements. The predictions show a linear growth of the shear layer. There is strong turbulence at the impingement, and the bulk of the turbulence kinetic energy is advected to the recirculation region via the shear layer. The predicted bottom-shear-stress distribution, with a peak value upstream of the toe of the jump and a decaying trend downstream, is realistic. This paper reveals a significant transient bottom shear stress associated with temporal fluctuations of mainly flow velocity in the jump. The prediction method discussed is useful for modelling hydraulic jumps and advancing the understanding of the complex flow phenomenon.

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Acknowledgements

Financial support from the Natural Sciences and Engineering Research Council of Canada through Discovery Grants held by S. Li is acknowledged. Comments from three anonymous reviewers are useful.

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Authors and Affiliations

  1. Department of Building, Civil and Environmental Engineering, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, QC, H3G 1M8, Canada

    Sho Harada & S. Samuel Li

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  1. Sho Harada
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  2. S. Samuel Li
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Correspondence to S. Samuel Li.

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Harada, S., Li, S.S. Modelling hydraulic jump using the bubbly two-phase flow method. Environ Fluid Mech 18, 335–356 (2018). https://doi.org/10.1007/s10652-017-9549-5

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